Abstract
We prove a superdiffusive central limit theorem for the displacement of a test particle in the periodic Lorentz gas in the limit of large times t and low scatterer densities (Boltzmann–Grad limit). The normalization factor is √tlogt, where t is measured in units of the mean collision time. This result holds in any dimension and for a general class of finiterange scattering potentials. We also establish the corresponding invariance principle, i.e., the weak convergence of the particle dynamics to Brownian motion.
Original language  English 

Pages (fromto)  933981 
Number of pages  49 
Journal  Communications in Mathematical Physics 
Volume  347 
Issue number  3 
Early online date  18 Feb 2016 
DOIs  
Publication status  Published  Nov 2016 
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Professor Balint A Toth
 School of Mathematics  Chair in Probability
 Probability, Analysis and Dynamics
 Probability
Person: Academic , Member, Group lead